So far we have discussed comparing the means of two populations to
each other and comparing the population mean to another number.
However, we often want to compare many populations to each other.

Example

We may want to compare regeneration rates for three
different tree species in northern Idaho. We would begin by taking
samples from each population and then calculate the means from the
three samples and make an inference about the population means from
this.

It is common since that these three mean regeneration rates would
all be different numbers however, this does not mean that there is a
difference between the population means for the three tree types.

To answer that question we can use a statistical test called an
analysis of variance or ANOVA. This test is widely used in natural
resources, and you are bound to come across it when reading
scientific literature.

The use of an ANOVA implies the following:

all the populations are normally distributed (follow a bell
shaped curve)

all the population variances are equal,

and all the samples were taken independently of each other and
are randomly collected from their population

Generally, our null hypothesis when conducting an ANOVA is that
all the population means are equal and our research hypothesis will
be that at least one of the population means is not equal.

Although an ANOVA is widely used and it does indicate that a
population mean is different than others, it does not tell us which
one is different from the others.